Yes you can surely watch videos on your PS2 using a flash drive. Just make sure that you have a flash drive that is compatible with the PS2. Because I have seen that many are not. I have a Kingston DATATRAVELER 8 GB and it works like a charm. Surprisingly, I have another Kingston DATATRAVELER 4 GB, which doesn't serve the purpose so well.
After you have your flash drive, its time to get this homebrew software called SMS Player, which is a multimedia player for your ps2.
You need to install this software on your PS2 Memory card(uLauchELF is used to do this.).
Now you may simply transfer the avi, mp4, divx or xvid video files on your flash drive from your computer and load the SMS PLAYER with the flash drive inserted into your PS2.
SMS Player is a very good multimedia player that gives you several options to have a good movie watching experience.
Hope this helps.
PS: For more details about homebrew stuff and about installing it, feel free to ask me on IM or Email.
All the best. Save your Laser:)